In [1]:
import cudf
import cupy as cp
import plotly.graph_objects as go
import datashader as ds
import colorcet
import os

# Visualisation Imports
import numpy as np
import xarray as xr
# datashader
import datashader as ds
import datashader.transfer_functions as tf
from datashader.transfer_functions import shade
from datashader.transfer_functions import stack
from datashader.transfer_functions import dynspread
from datashader.transfer_functions import set_background
from datashader.transfer_functions import Images, Image
from datashader.colors import Elevation
from datashader.utils import orient_array

# holoviews
import holoviews as hv
from holoviews.plotting.plotly.dash import to_dash
from holoviews.element.tiles import CartoDark
from holoviews.operation.datashader import datashade, shade, dynspread, spread, rasterize
from holoviews.operation import decimate

# plotly
from plotly.colors import sequential
from plotly.subplots import make_subplots

# Dash Import
import dash
import dash_html_components as html
from jupyter_dash import JupyterDash
In [2]:
DATA_PATH = '../../data/hycom'
RES_PATH = '../../results/hycom'

df = cudf.read_csv(os.path.join(RES_PATH, 'hycom_equinox_merged-201920.csv'))
df.head()
Out[2]:
start_date lat lon water_temp_0 salinity_0 water_temp_2 salinity_2 water_temp_4 salinity_4 water_temp_6 ... xCO2_ATM_interpolated_ppm PRES_EQU_hPa PRES_ATM@SSP_hPa TEMP_EQU_C SST_C SAL_permil fCO2_SW@SST_uatm fCO2_ATM_interpolated_uatm dfCO2_uatm WOCE_QC_FLAG
0 2019-11-19 19.0418 -87.4192 28.641375 36.191375 28.48175 36.194000 28.490375 36.193750 28.494625 ... 410.81 1014.72 1013.5662 29.14 29.1692 36.2848 410.02 393.66 16.36 2.0
1 2020-01-21 18.3305 -65.1468 26.471600 35.826667 26.42980 35.825867 26.429333 35.828200 26.426533 ... 417.55 1015.40 1014.5055 27.25 27.3215 35.3726 390.25 402.13 -11.88 2.0
2 2019-07-31 19.7638 -87.1375 29.324125 36.082625 29.24825 36.083875 29.235125 36.083500 29.218875 ... 410.89 1014.90 1014.5565 29.98 29.7258 36.2400 435.94 393.63 42.32 2.0
3 2019-09-13 25.9173 -79.9605 29.782625 36.122750 29.79925 36.123500 29.802750 36.124125 29.803750 ... 414.53 1012.47 1011.9442 29.88 29.9378 35.4666 413.24 395.84 17.40 2.0
4 2019-08-11 23.2150 -83.5792 30.861500 36.154125 30.54200 36.152875 30.412500 36.150375 30.245500 ... 417.82 1017.40 1017.0594 30.57 30.6395 36.3900 442.06 400.40 41.66 2.0

5 rows × 26 columns

In [3]:
df = df[df['WOCE_QC_FLAG'] == 2]
In [4]:
df.head()
Out[4]:
start_date lat lon water_temp_0 salinity_0 water_temp_2 salinity_2 water_temp_4 salinity_4 water_temp_6 ... xCO2_ATM_interpolated_ppm PRES_EQU_hPa PRES_ATM@SSP_hPa TEMP_EQU_C SST_C SAL_permil fCO2_SW@SST_uatm fCO2_ATM_interpolated_uatm dfCO2_uatm WOCE_QC_FLAG
0 2019-11-19 19.0418 -87.4192 28.641375 36.191375 28.48175 36.194000 28.490375 36.193750 28.494625 ... 410.81 1014.72 1013.5662 29.14 29.1692 36.2848 410.02 393.66 16.36 2.0
1 2020-01-21 18.3305 -65.1468 26.471600 35.826667 26.42980 35.825867 26.429333 35.828200 26.426533 ... 417.55 1015.40 1014.5055 27.25 27.3215 35.3726 390.25 402.13 -11.88 2.0
2 2019-07-31 19.7638 -87.1375 29.324125 36.082625 29.24825 36.083875 29.235125 36.083500 29.218875 ... 410.89 1014.90 1014.5565 29.98 29.7258 36.2400 435.94 393.63 42.32 2.0
3 2019-09-13 25.9173 -79.9605 29.782625 36.122750 29.79925 36.123500 29.802750 36.124125 29.803750 ... 414.53 1012.47 1011.9442 29.88 29.9378 35.4666 413.24 395.84 17.40 2.0
4 2019-08-11 23.2150 -83.5792 30.861500 36.154125 30.54200 36.152875 30.412500 36.150375 30.245500 ... 417.82 1017.40 1017.0594 30.57 30.6395 36.3900 442.06 400.40 41.66 2.0

5 rows × 26 columns

Exploring Interaction between Sentinel (Satellite Data) on ground-truth labels (Equinox)¶

Dropping date, lat and lon since these are not expected to significantly impact relationships

In [5]:
df.drop(['start_date', 'lat', 'lon', 'WOCE_QC_FLAG', 'easting', 'northing'], axis=1, inplace=True)
df.head()
Out[5]:
water_temp_0 salinity_0 water_temp_2 salinity_2 water_temp_4 salinity_4 water_temp_6 salinity_6 water_temp_8 salinity_8 xCO2_EQU_ppm xCO2_ATM_interpolated_ppm PRES_EQU_hPa PRES_ATM@SSP_hPa TEMP_EQU_C SST_C SAL_permil fCO2_SW@SST_uatm fCO2_ATM_interpolated_uatm dfCO2_uatm
0 28.641375 36.191375 28.48175 36.194000 28.490375 36.193750 28.494625 36.193500 28.495625 36.193250 426.816 410.81 1014.72 1013.5662 29.14 29.1692 36.2848 410.02 393.66 16.36
1 26.471600 35.826667 26.42980 35.825867 26.429333 35.828200 26.426533 35.830333 26.422667 35.832533 403.554 417.55 1015.40 1014.5055 27.25 27.3215 35.3726 390.25 402.13 -11.88
2 29.324125 36.082625 29.24825 36.083875 29.235125 36.083500 29.218875 36.083000 29.198750 36.082250 460.100 410.89 1014.90 1014.5565 29.98 29.7258 36.2400 435.94 393.63 42.32
3 29.782625 36.122750 29.79925 36.123500 29.802750 36.124125 29.803750 36.124375 29.803375 36.124375 431.397 414.53 1012.47 1011.9442 29.88 29.9378 35.4666 413.24 395.84 17.40
4 30.861500 36.154125 30.54200 36.152875 30.412500 36.150375 30.245500 36.148625 29.899750 36.150000 459.698 417.82 1017.40 1017.0594 30.57 30.6395 36.3900 442.06 400.40 41.66
In [7]:
from statsmodels.regression import linear_model
import pandas as pd
from sklearn.preprocessing import PolynomialFeatures

X_col_names = ['water_temp_0', 'salinity_0', 'water_temp_2', 'salinity_2', 'water_temp_4', 'salinity_4', 'water_temp_6', 'salinity_6', 'water_temp_8', 'salinity_8']


def fit_model(df, pred_col):
    X = df[X_col_names]
    y = df[[col]]
    
    model = linear_model.OLS(y, X).fit()
    print(model_summary)
    
def fit_interaction_model(df, pred_col):
    
    df = df.dropna()
    
    X = df[X_col_names]
    y = df[[pred_col]]
    poly_features = PolynomialFeatures(2, interaction_only=True, include_bias=False) 
    X_inter = poly_features.fit_transform(X.as_gpu_matrix())
    X_df = cudf.DataFrame(X_inter, columns=poly_features.get_feature_names(X.columns))
    inter_model = linear_model.OLS(y.to_pandas().values, X_df.to_pandas()).fit()
#     inter_model = inter_model.pvalues[inter_model.pvalues < 0.05]
    print(inter_model.summary())

Plotting Interaction Columns¶

In [36]:
df = df.dropna()

X = df[X_col_names]

equinox_col_names = dict({
    'xCO2_EQU_ppm': 'Mole fraction of CO2 in the equilibrator headspace (ppm)', 
    'xCO2_ATM_interpolated_ppm': 'Mole fraction of CO2 measured in dry outside air (ppm)',
    'PRES_EQU_hPa': 'Barometric pressure in the equilibrator headspace (hPa)', 
    'PRES_ATM@SSP_hPa':  'Barometric pressure measured outside, corrected to sea level (hPa)',
    'TEMP_EQU_C': 'Water temperature in equilibrator (°C)', 
    'SST_C': 'Sea surface temperature (°C)',
    'SAL_permil': 'Sea surface salinity on Practical Salinity Scale (ppt)',
    'fCO2_SW@SST_uatm': 'Fugacity of CO2 in sea water at SST and 100% humidity (μatm)',
    'fCO2_ATM_interpolated_uatm': 'Fugacity of CO2 in air corresponding to the interpolated xCO2 at SST and 100% humidity (μatm)',
    'dfCO2_uatm': 'Sea water fCO2 minus interpolated air fCO2 (μatm)' ,
    })


poly_features = PolynomialFeatures(2, interaction_only=True, include_bias=False) 
X_inter = poly_features.fit_transform(X.as_gpu_matrix())
X_inter_cols = poly_features.get_feature_names(X.columns)
X_df = cudf.DataFrame(X_inter, columns=poly_features.get_feature_names(X.columns))


def plot_correlation(df, hycom_col):
    graph_list = []
    
    data = pd.concat([X_df.to_pandas(), df[hycom_col].to_pandas()], axis=1)    
    hv_data = hv.Dataset(data)
    
    for idx, col in enumerate(X_inter_cols):
        scatter = hv.Scatter(hv_data, kdims=col, vdims=hycom_col).opts(width=600, height=400, title=equinox_col_names[hycom_col])
        scatter.redim(y=hv.Dimension(col))
        shaded = decimate(scatter, y_range=(0, data[hycom_col].max())).opts(width=600,  height=400)
        graph_list.append(shaded)
        del scatter
        
    layout = hv.Layout(graph_list).cols(2)
    return layout
    

plot_correlation(df, 'xCO2_EQU_ppm')
Out[36]:
In [37]:
plot_correlation(df, 'xCO2_ATM_interpolated_ppm')
Parameter name clashes for keys ['x_range']
Parameter name clashes for keys ['x_range']
Out[37]:
In [38]:
plot_correlation(df, 'fCO2_SW@SST_uatm')
Out[38]:
In [39]:
plot_correlation(df, 'fCO2_ATM_interpolated_uatm')
Parameter name clashes for keys ['x_range']
Parameter name clashes for keys ['x_range']
Out[39]:
In [40]:
plot_correlation(df, 'dfCO2_uatm')
Parameter name clashes for keys ['x_range']
Parameter name clashes for keys ['x_range']
Parameter name clashes for keys ['x_range']
Parameter name clashes for keys ['x_range']
Parameter name clashes for keys ['x_range']
Parameter name clashes for keys ['x_range']
Out[40]:
In [60]:
fit_interaction_model(df, 'xCO2_ATM_interpolated_ppm')

                                 OLS Regression Results                                
=======================================================================================
Dep. Variable:                      y   R-squared (uncentered):                   0.566
Model:                            OLS   Adj. R-squared (uncentered):              0.565
Method:                 Least Squares   F-statistic:                              2694.
Date:                Tue, 15 Jun 2021   Prob (F-statistic):                        0.00
Time:                        19:56:38   Log-Likelihood:                     -8.1238e+05
No. Observations:              113837   AIC:                                  1.625e+06
Df Residuals:                  113782   BIC:                                  1.625e+06
Df Model:                          55                                                  
Covariance Type:            nonrobust                                                  
=============================================================================================
                                coef    std err          t      P>|t|      [0.025      0.975]
---------------------------------------------------------------------------------------------
water_temp_0               2117.2401   2485.582      0.852      0.394   -2754.463    6988.943
salinity_0                -6.688e+04   6.74e+04     -0.993      0.321   -1.99e+05    6.52e+04
water_temp_2              -5327.7334   1.03e+04     -0.518      0.605   -2.55e+04    1.48e+04
salinity_2                 9.175e+04   1.56e+05      0.588      0.557   -2.14e+05    3.98e+05
water_temp_4              -1.936e+04    2.6e+04     -0.743      0.457   -7.04e+04    3.17e+04
salinity_4                -8813.0707   2.59e+05     -0.034      0.973   -5.17e+05       5e+05
water_temp_6               3.594e+04   2.67e+04      1.347      0.178   -1.63e+04    8.82e+04
salinity_6                -4.096e+04    2.2e+05     -0.186      0.853   -4.73e+05    3.91e+05
water_temp_8              -1.343e+04      1e+04     -1.341      0.180   -3.31e+04    6205.813
salinity_8                 2.495e+04   6.03e+04      0.413      0.679   -9.33e+04    1.43e+05
water_temp_0 salinity_0    1631.3642   5834.485      0.280      0.780   -9804.137    1.31e+04
water_temp_0 water_temp_2   633.3594    369.572      1.714      0.087     -90.995    1357.714
water_temp_0 salinity_2   -1.687e+04   1.18e+04     -1.434      0.152   -3.99e+04    6187.248
water_temp_0 water_temp_4 -1601.6124   1638.801     -0.977      0.328   -4813.637    1610.412
water_temp_0 salinity_4    2795.3105   2.71e+04      0.103      0.918   -5.04e+04     5.6e+04
water_temp_0 water_temp_6   365.1563   2177.643      0.168      0.867   -3902.990    4633.303
water_temp_0 salinity_6    2.233e+04   2.43e+04      0.918      0.359   -2.54e+04       7e+04
water_temp_0 water_temp_8   668.6167    879.669      0.760      0.447   -1055.520    2392.754
water_temp_0 salinity_8       -1e+04   5806.418     -1.722      0.085   -2.14e+04    1378.965
salinity_0 water_temp_2   -1.865e+04   3.01e+04     -0.619      0.536   -7.77e+04    4.04e+04
salinity_0 salinity_2     -2.888e+04   3.43e+04     -0.843      0.399    -9.6e+04    3.83e+04
salinity_0 water_temp_4      1.9e+05   9.37e+04      2.028      0.043    6402.860    3.74e+05
salinity_0 salinity_4      4.244e+05   3.42e+05      1.241      0.214   -2.46e+05    1.09e+06
salinity_0 water_temp_6   -2.665e+05    9.8e+04     -2.719      0.007   -4.59e+05   -7.44e+04
salinity_0 salinity_6     -4.205e+05    4.1e+05     -1.025      0.306   -1.22e+06    3.84e+05
salinity_0 water_temp_8    9.418e+04   3.45e+04      2.732      0.006    2.66e+04    1.62e+05
salinity_0 salinity_8      2.631e+04   1.29e+05      0.204      0.838   -2.26e+05    2.79e+05
water_temp_2 salinity_2     5.94e+04   5.45e+04      1.091      0.275   -4.73e+04    1.66e+05
water_temp_2 water_temp_4 -1638.5309   1641.885     -0.998      0.318   -4856.600    1579.538
water_temp_2 salinity_4   -1.243e+05   8.48e+04     -1.466      0.143    -2.9e+05    4.19e+04
water_temp_2 water_temp_6  5115.3098   3497.749      1.462      0.144   -1740.226     1.2e+04
water_temp_2 salinity_6    7.401e+04   7.33e+04      1.010      0.312   -6.96e+04    2.18e+05
water_temp_2 water_temp_8 -4374.1540   2065.173     -2.118      0.034   -8421.862    -326.446
water_temp_2 salinity_8    9884.7059   1.72e+04      0.573      0.566   -2.39e+04    4.37e+04
salinity_2 water_temp_4   -4.011e+05   1.72e+05     -2.328      0.020   -7.39e+05   -6.34e+04
salinity_2 salinity_4     -4.525e+05   3.37e+05     -1.343      0.179   -1.11e+06    2.08e+05
salinity_2 water_temp_6    5.628e+05   1.87e+05      3.008      0.003    1.96e+05    9.29e+05
salinity_2 salinity_6      6.468e+05    5.1e+05      1.268      0.205   -3.53e+05    1.65e+06
salinity_2 water_temp_8   -2.053e+05   6.94e+04     -2.960      0.003   -3.41e+05   -6.94e+04
salinity_2 salinity_8      -1.67e+05   2.03e+05     -0.823      0.411   -5.65e+05    2.31e+05
water_temp_4 salinity_4    5.431e+05   2.23e+05      2.437      0.015    1.06e+05     9.8e+05
water_temp_4 water_temp_6 -2998.6293   1484.430     -2.020      0.043   -5908.090     -89.169
water_temp_4 salinity_6   -3.773e+05    1.7e+05     -2.218      0.027   -7.11e+05   -4.38e+04
water_temp_4 water_temp_8  6882.3059   2350.781      2.928      0.003    2274.812    1.15e+04
water_temp_4 salinity_8    4.534e+04      4e+04      1.133      0.257   -3.31e+04    1.24e+05
salinity_4 water_temp_6   -5.898e+05   2.33e+05     -2.533      0.011   -1.05e+06   -1.33e+05
salinity_4 salinity_6     -1.693e+05   1.22e+05     -1.390      0.164   -4.08e+05    6.93e+04
salinity_4 water_temp_8    1.684e+05   8.73e+04      1.931      0.054   -2572.577    3.39e+05
salinity_4 salinity_8      1.973e+05    1.4e+05      1.410      0.158   -7.69e+04    4.71e+05
water_temp_6 salinity_6    3.567e+05   1.61e+05      2.214      0.027     4.1e+04    6.73e+05
water_temp_6 water_temp_8 -3051.0309    881.856     -3.460      0.001   -4779.454   -1322.607
water_temp_6 salinity_8   -6.378e+04   3.33e+04     -1.915      0.056   -1.29e+05    1510.171
salinity_6 water_temp_8   -7.484e+04    5.8e+04     -1.291      0.197   -1.88e+05    3.88e+04
salinity_6 salinity_8     -5.672e+04   5.34e+04     -1.063      0.288   -1.61e+05    4.79e+04
water_temp_8 salinity_8    1.782e+04   9849.164      1.810      0.070   -1481.644    3.71e+04
==============================================================================
Omnibus:                    93819.299   Durbin-Watson:                   1.999
Prob(Omnibus):                  0.000   Jarque-Bera (JB):          1479030.029
Skew:                          -4.183   Prob(JB):                         0.00
Kurtosis:                      18.550   Cond. No.                     6.36e+09
==============================================================================

Notes:
[1] R² is computed without centering (uncentered) since the model does not contain a constant.
[2] Standard Errors assume that the covariance matrix of the errors is correctly specified.
[3] The condition number is large, 6.36e+09. This might indicate that there are
strong multicollinearity or other numerical problems.
In [ ]:
In [ ]:
# equinox_cols = ['xCO2_EQU_ppm',
#  'xCO2_ATM_interpolated_ppm',
#  'PRES_EQU_hPa',
#  'PRES_ATM@SSP_hPa',
#  'TEMP_EQU_C',
#  'SST_C',
#  'SAL_permil',
#  'fCO2_SW@SST_uatm',
#  'fCO2_ATM_interpolated_uatm',
#  'dfCO2_uatm']

fit_interaction_model(df, 'xCO2_ATM_interpolated_ppm')
In [61]:
fit_interaction_model(df, 'PRES_EQU_hPa')

                                 OLS Regression Results                                
=======================================================================================
Dep. Variable:                      y   R-squared (uncentered):                   0.818
Model:                            OLS   Adj. R-squared (uncentered):              0.818
Method:                 Least Squares   F-statistic:                              9305.
Date:                Tue, 15 Jun 2021   Prob (F-statistic):                        0.00
Time:                        19:58:25   Log-Likelihood:                     -8.5273e+05
No. Observations:              113837   AIC:                                  1.706e+06
Df Residuals:                  113782   BIC:                                  1.706e+06
Df Model:                          55                                                  
Covariance Type:            nonrobust                                                  
=============================================================================================
                                coef    std err          t      P>|t|      [0.025      0.975]
---------------------------------------------------------------------------------------------
water_temp_0               3027.9221   3542.791      0.855      0.393   -3915.895    9971.740
salinity_0                -8.197e+04    9.6e+04     -0.854      0.393    -2.7e+05    1.06e+05
water_temp_2              -1.161e+04   1.47e+04     -0.792      0.428   -4.04e+04    1.71e+04
salinity_2                 1.667e+05   2.22e+05      0.749      0.454   -2.69e+05    6.03e+05
water_temp_4              -1.132e+04   3.71e+04     -0.305      0.760   -8.41e+04    6.14e+04
salinity_4                -8.042e+04    3.7e+05     -0.218      0.828   -8.05e+05    6.44e+05
water_temp_6               3.353e+04    3.8e+04      0.882      0.378    -4.1e+04    1.08e+05
salinity_6                -4.579e+04   3.14e+05     -0.146      0.884   -6.61e+05     5.7e+05
water_temp_8              -1.363e+04   1.43e+04     -0.955      0.340   -4.16e+04    1.44e+04
salinity_8                 4.154e+04    8.6e+04      0.483      0.629   -1.27e+05     2.1e+05
water_temp_0 salinity_0    2546.0588   8316.105      0.306      0.759   -1.38e+04    1.88e+04
water_temp_0 water_temp_2   844.8312    526.764      1.604      0.109    -187.618    1877.280
water_temp_0 salinity_2   -2.347e+04   1.68e+04     -1.400      0.162   -5.63e+04    9392.139
water_temp_0 water_temp_4 -1337.6896   2335.843     -0.573      0.567   -5915.906    3240.527
water_temp_0 salinity_4    7510.5214   3.87e+04      0.194      0.846   -6.83e+04    8.33e+04
water_temp_0 water_temp_6  -852.0921   3103.874     -0.275      0.784   -6935.638    5231.454
water_temp_0 salinity_6    2.702e+04   3.47e+04      0.779      0.436    -4.1e+04     9.5e+04
water_temp_0 water_temp_8  1440.8890   1253.824      1.149      0.250   -1016.587    3898.365
water_temp_0 salinity_8   -1.377e+04   8276.101     -1.664      0.096      -3e+04    2450.110
salinity_0 water_temp_2   -2.671e+04   4.29e+04     -0.622      0.534   -1.11e+05    5.75e+04
salinity_0 salinity_2     -3.323e+04   4.88e+04     -0.681      0.496   -1.29e+05    6.25e+04
salinity_0 water_temp_4    2.779e+05   1.34e+05      2.082      0.037    1.62e+04     5.4e+05
salinity_0 salinity_4      5.907e+05   4.87e+05      1.212      0.225   -3.64e+05    1.55e+06
salinity_0 water_temp_6   -4.005e+05    1.4e+05     -2.867      0.004   -6.74e+05   -1.27e+05
salinity_0 salinity_6     -6.186e+05   5.85e+05     -1.058      0.290   -1.77e+06    5.28e+05
salinity_0 water_temp_8    1.474e+05   4.91e+04      3.001      0.003    5.11e+04    2.44e+05
salinity_0 salinity_8      6.292e+04   1.84e+05      0.342      0.732   -2.97e+05    4.23e+05
water_temp_2 salinity_2    8.064e+04   7.76e+04      1.039      0.299   -7.15e+04    2.33e+05
water_temp_2 water_temp_4 -3028.1460   2340.238     -1.294      0.196   -7614.978    1558.686
water_temp_2 salinity_4   -1.784e+05   1.21e+05     -1.476      0.140   -4.15e+05    5.85e+04
water_temp_2 water_temp_6  8916.7328   4985.471      1.789      0.074    -854.714    1.87e+04
water_temp_2 salinity_6    1.148e+05   1.04e+05      1.099      0.272   -8.99e+04    3.19e+05
water_temp_2 water_temp_8 -7104.1989   2943.567     -2.413      0.016   -1.29e+04   -1334.852
water_temp_2 salinity_8    1.026e+04   2.46e+04      0.417      0.676   -3.79e+04    5.84e+04
salinity_2 water_temp_4   -5.768e+05   2.46e+05     -2.348      0.019   -1.06e+06   -9.54e+04
salinity_2 salinity_4     -6.321e+05    4.8e+05     -1.317      0.188   -1.57e+06    3.09e+05
salinity_2 water_temp_6    8.323e+05   2.67e+05      3.121      0.002     3.1e+05    1.36e+06
salinity_2 salinity_6      9.227e+05   7.27e+05      1.269      0.204   -5.02e+05    2.35e+06
salinity_2 water_temp_8   -3.145e+05   9.89e+04     -3.181      0.001   -5.08e+05   -1.21e+05
salinity_2 salinity_8     -2.605e+05   2.89e+05     -0.901      0.368   -8.27e+05    3.06e+05
water_temp_4 salinity_4    7.612e+05   3.18e+05      2.396      0.017    1.39e+05    1.38e+06
water_temp_4 water_temp_6 -4671.1997   2115.813     -2.208      0.027   -8818.161    -524.239
water_temp_4 salinity_6   -5.343e+05   2.42e+05     -2.204      0.028   -1.01e+06   -5.91e+04
water_temp_4 water_temp_8  9864.9775   3350.654      2.944      0.003    3297.746    1.64e+04
water_temp_4 salinity_8    7.166e+04    5.7e+04      1.257      0.209   -4.01e+04    1.83e+05
salinity_4 water_temp_6   -8.314e+05   3.32e+05     -2.505      0.012   -1.48e+06   -1.81e+05
salinity_4 salinity_6     -2.293e+05   1.74e+05     -1.322      0.186   -5.69e+05    1.11e+05
salinity_4 water_temp_8    2.411e+05   1.24e+05      1.939      0.053   -2658.627    4.85e+05
salinity_4 salinity_8      2.728e+05   1.99e+05      1.368      0.171   -1.18e+05    6.64e+05
water_temp_6 salinity_6    4.938e+05    2.3e+05      2.150      0.032    4.37e+04    9.44e+05
water_temp_6 water_temp_8 -4073.9961   1256.941     -3.241      0.001   -6537.582   -1610.411
water_temp_6 salinity_8   -9.468e+04   4.75e+04     -1.994      0.046   -1.88e+05   -1618.197
salinity_6 water_temp_8   -9.907e+04   8.26e+04     -1.199      0.230   -2.61e+05    6.29e+04
salinity_6 salinity_8     -7.531e+04   7.61e+04     -0.990      0.322   -2.24e+05    7.38e+04
water_temp_8 salinity_8     2.53e+04    1.4e+04      1.803      0.071   -2210.439    5.28e+04
==============================================================================
Omnibus:                    93891.307   Durbin-Watson:                   1.999
Prob(Omnibus):                  0.000   Jarque-Bera (JB):          1481982.320
Skew:                          -4.188   Prob(JB):                         0.00
Kurtosis:                      18.566   Cond. No.                     6.36e+09
==============================================================================

Notes:
[1] R² is computed without centering (uncentered) since the model does not contain a constant.
[2] Standard Errors assume that the covariance matrix of the errors is correctly specified.
[3] The condition number is large, 6.36e+09. This might indicate that there are
strong multicollinearity or other numerical problems.
In [62]:
fit_interaction_model(df, 'PRES_ATM@SSP_hPa')

                                 OLS Regression Results                                
=======================================================================================
Dep. Variable:                      y   R-squared (uncentered):                   0.818
Model:                            OLS   Adj. R-squared (uncentered):              0.818
Method:                 Least Squares   F-statistic:                              9295.
Date:                Tue, 15 Jun 2021   Prob (F-statistic):                        0.00
Time:                        19:58:26   Log-Likelihood:                     -8.5267e+05
No. Observations:              113837   AIC:                                  1.705e+06
Df Residuals:                  113782   BIC:                                  1.706e+06
Df Model:                          55                                                  
Covariance Type:            nonrobust                                                  
=============================================================================================
                                coef    std err          t      P>|t|      [0.025      0.975]
---------------------------------------------------------------------------------------------
water_temp_0               3005.9790   3541.034      0.849      0.396   -3934.393    9946.351
salinity_0                -8.267e+04    9.6e+04     -0.861      0.389   -2.71e+05    1.05e+05
water_temp_2              -1.147e+04   1.47e+04     -0.782      0.434   -4.02e+04    1.73e+04
salinity_2                 1.663e+05   2.22e+05      0.748      0.455    -2.7e+05    6.02e+05
water_temp_4              -1.186e+04   3.71e+04     -0.320      0.749   -8.46e+04    6.08e+04
salinity_4                -8.017e+04    3.7e+05     -0.217      0.828   -8.04e+05    6.44e+05
water_temp_6               3.371e+04    3.8e+04      0.887      0.375   -4.08e+04    1.08e+05
salinity_6                -4.437e+04   3.14e+05     -0.141      0.888    -6.6e+05    5.71e+05
water_temp_8              -1.338e+04   1.43e+04     -0.937      0.349   -4.14e+04    1.46e+04
salinity_8                 4.098e+04    8.6e+04      0.477      0.634   -1.28e+05    2.09e+05
water_temp_0 salinity_0    2682.9987   8311.979      0.323      0.747   -1.36e+04     1.9e+04
water_temp_0 water_temp_2   836.3581    526.503      1.589      0.112    -195.579    1868.295
water_temp_0 salinity_2   -2.367e+04   1.68e+04     -1.413      0.158   -5.65e+04    9173.286
water_temp_0 water_temp_4 -1316.7359   2334.684     -0.564      0.573   -5892.681    3259.209
water_temp_0 salinity_4    7424.8887   3.86e+04      0.192      0.848   -6.83e+04    8.32e+04
water_temp_0 water_temp_6  -872.6940   3102.334     -0.281      0.778   -6953.222    5207.834
water_temp_0 salinity_6    2.716e+04   3.47e+04      0.784      0.433   -4.08e+04    9.51e+04
water_temp_0 water_temp_8  1448.9436   1253.202      1.156      0.248   -1007.313    3905.200
water_temp_0 salinity_8   -1.376e+04   8271.995     -1.664      0.096      -3e+04    2452.102
salinity_0 water_temp_2   -2.772e+04   4.29e+04     -0.646      0.518   -1.12e+05    5.64e+04
salinity_0 salinity_2     -3.364e+04   4.88e+04     -0.689      0.491   -1.29e+05     6.2e+04
salinity_0 water_temp_4    2.812e+05   1.33e+05      2.107      0.035    1.97e+04    5.43e+05
salinity_0 salinity_4      5.924e+05   4.87e+05      1.216      0.224   -3.62e+05    1.55e+06
salinity_0 water_temp_6   -4.035e+05    1.4e+05     -2.891      0.004   -6.77e+05    -1.3e+05
salinity_0 salinity_6     -6.201e+05   5.85e+05     -1.061      0.289   -1.77e+06    5.26e+05
salinity_0 water_temp_8    1.481e+05   4.91e+04      3.015      0.003    5.18e+04    2.44e+05
salinity_0 salinity_8      6.314e+04   1.84e+05      0.344      0.731   -2.97e+05    4.23e+05
water_temp_2 salinity_2    8.223e+04   7.76e+04      1.060      0.289   -6.98e+04    2.34e+05
water_temp_2 water_temp_4 -3021.3994   2339.077     -1.292      0.196   -7605.956    1563.157
water_temp_2 salinity_4    -1.78e+05   1.21e+05     -1.474      0.140   -4.15e+05    5.87e+04
water_temp_2 water_temp_6  8913.3252   4982.997      1.789      0.074    -853.274    1.87e+04
water_temp_2 salinity_6    1.138e+05   1.04e+05      1.090      0.276   -9.08e+04    3.18e+05
water_temp_2 water_temp_8 -7099.9697   2942.107     -2.413      0.016   -1.29e+04   -1333.485
water_temp_2 salinity_8    1.034e+04   2.46e+04      0.421      0.674   -3.78e+04    5.85e+04
salinity_2 water_temp_4   -5.823e+05   2.45e+05     -2.372      0.018   -1.06e+06   -1.01e+05
salinity_2 salinity_4     -6.348e+05    4.8e+05     -1.323      0.186   -1.58e+06    3.06e+05
salinity_2 water_temp_6    8.377e+05   2.67e+05      3.143      0.002    3.15e+05    1.36e+06
salinity_2 salinity_6      9.276e+05   7.27e+05      1.277      0.202   -4.97e+05    2.35e+06
salinity_2 water_temp_8   -3.156e+05   9.88e+04     -3.194      0.001   -5.09e+05   -1.22e+05
salinity_2 salinity_8     -2.623e+05   2.89e+05     -0.907      0.364   -8.29e+05    3.04e+05
water_temp_4 salinity_4    7.623e+05   3.18e+05      2.401      0.016     1.4e+05    1.38e+06
water_temp_4 water_temp_6 -4666.2528   2114.763     -2.207      0.027   -8811.156    -521.349
water_temp_4 salinity_6   -5.328e+05   2.42e+05     -2.199      0.028   -1.01e+06   -5.78e+04
water_temp_4 water_temp_8  9841.5523   3348.992      2.939      0.003    3277.580    1.64e+04
water_temp_4 salinity_8    7.137e+04    5.7e+04      1.252      0.210   -4.03e+04    1.83e+05
salinity_4 water_temp_6   -8.331e+05   3.32e+05     -2.512      0.012   -1.48e+06   -1.83e+05
salinity_4 salinity_6     -2.313e+05   1.73e+05     -1.334      0.182   -5.71e+05    1.09e+05
salinity_4 water_temp_8    2.416e+05   1.24e+05      1.944      0.052   -2044.246    4.85e+05
salinity_4 salinity_8      2.757e+05   1.99e+05      1.383      0.167   -1.15e+05    6.66e+05
water_temp_6 salinity_6    4.931e+05    2.3e+05      2.148      0.032    4.32e+04    9.43e+05
water_temp_6 water_temp_8 -4063.0526   1256.317     -3.234      0.001   -6525.416   -1600.689
water_temp_6 salinity_8   -9.454e+04   4.75e+04     -1.992      0.046   -1.88e+05   -1520.310
salinity_6 water_temp_8   -9.915e+04   8.26e+04     -1.201      0.230   -2.61e+05    6.27e+04
salinity_6 salinity_8     -7.672e+04    7.6e+04     -1.009      0.313   -2.26e+05    7.23e+04
water_temp_8 salinity_8    2.538e+04    1.4e+04      1.809      0.070   -2120.526    5.29e+04
==============================================================================
Omnibus:                    93891.855   Durbin-Watson:                   1.999
Prob(Omnibus):                  0.000   Jarque-Bera (JB):          1482011.308
Skew:                          -4.188   Prob(JB):                         0.00
Kurtosis:                      18.566   Cond. No.                     6.36e+09
==============================================================================

Notes:
[1] R² is computed without centering (uncentered) since the model does not contain a constant.
[2] Standard Errors assume that the covariance matrix of the errors is correctly specified.
[3] The condition number is large, 6.36e+09. This might indicate that there are
strong multicollinearity or other numerical problems.
In [63]:
fit_interaction_model(df, 'TEMP_EQU_C')

                                 OLS Regression Results                                
=======================================================================================
Dep. Variable:                      y   R-squared (uncentered):                   0.011
Model:                            OLS   Adj. R-squared (uncentered):              0.011
Method:                 Least Squares   F-statistic:                              23.59
Date:                Tue, 15 Jun 2021   Prob (F-statistic):                   1.00e-233
Time:                        19:58:28   Log-Likelihood:                     -7.7592e+05
No. Observations:              113837   AIC:                                  1.552e+06
Df Residuals:                  113782   BIC:                                  1.552e+06
Df Model:                          55                                                  
Covariance Type:            nonrobust                                                  
=============================================================================================
                                coef    std err          t      P>|t|      [0.025      0.975]
---------------------------------------------------------------------------------------------
water_temp_0               1397.3877   1804.251      0.774      0.439   -2138.916    4933.692
salinity_0                -4.485e+04   4.89e+04     -0.917      0.359   -1.41e+05     5.1e+04
water_temp_2              -5294.4108   7467.864     -0.709      0.478   -1.99e+04    9342.490
salinity_2                 8.486e+04   1.13e+05      0.749      0.454   -1.37e+05    3.07e+05
water_temp_4              -6947.5498   1.89e+04     -0.368      0.713    -4.4e+04    3.01e+04
salinity_4                 -3.07e+04   1.88e+05     -0.163      0.870      -4e+05    3.38e+05
water_temp_6               1.866e+04   1.94e+04      0.964      0.335   -1.93e+04    5.66e+04
salinity_6                 -2.94e+04    1.6e+05     -0.184      0.854   -3.43e+05    2.84e+05
water_temp_8              -7804.7857   7273.118     -1.073      0.283   -2.21e+04    6450.416
salinity_8                 2.007e+04   4.38e+04      0.458      0.647   -6.58e+04    1.06e+05
water_temp_0 salinity_0    1570.5106   4235.174      0.371      0.711   -6730.366    9871.388
water_temp_0 water_temp_2   401.0032    268.267      1.495      0.135    -124.796     926.803
water_temp_0 salinity_2   -1.195e+04   8537.676     -1.400      0.162   -2.87e+04    4783.172
water_temp_0 water_temp_4  -650.9287   1189.583     -0.547      0.584   -2982.494    1680.637
water_temp_0 salinity_4    2941.0882   1.97e+04      0.149      0.881   -3.57e+04    4.15e+04
water_temp_0 water_temp_6  -414.8093   1580.722     -0.262      0.793   -3513.000    2683.381
water_temp_0 salinity_6    1.452e+04   1.77e+04      0.822      0.411   -2.01e+04    4.91e+04
water_temp_0 water_temp_8   713.1715    638.540      1.117      0.264    -538.356    1964.700
water_temp_0 salinity_8   -7157.0100   4214.801     -1.698      0.089   -1.54e+04    1103.936
salinity_0 water_temp_2   -1.479e+04   2.19e+04     -0.676      0.499   -5.77e+04    2.81e+04
salinity_0 salinity_2     -1.702e+04   2.49e+04     -0.684      0.494   -6.58e+04    3.17e+04
salinity_0 water_temp_4    1.419e+05    6.8e+04      2.086      0.037    8598.585    2.75e+05
salinity_0 salinity_4      2.928e+05   2.48e+05      1.180      0.238   -1.94e+05    7.79e+05
salinity_0 water_temp_6    -2.03e+05   7.11e+04     -2.854      0.004   -3.42e+05   -6.36e+04
salinity_0 salinity_6     -3.057e+05   2.98e+05     -1.026      0.305   -8.89e+05    2.78e+05
salinity_0 water_temp_8    7.474e+04    2.5e+04      2.987      0.003    2.57e+04    1.24e+05
salinity_0 salinity_8      3.077e+04   9.36e+04      0.329      0.742   -1.53e+05    2.14e+05
water_temp_2 salinity_2    4.413e+04   3.95e+04      1.116      0.264   -3.33e+04    1.22e+05
water_temp_2 water_temp_4 -1479.7946   1191.822     -1.242      0.214   -3815.748     856.158
water_temp_2 salinity_4   -9.226e+04   6.15e+04     -1.499      0.134   -2.13e+05    2.84e+04
water_temp_2 water_temp_6  4411.5002   2538.969      1.738      0.082    -564.841    9387.842
water_temp_2 salinity_6    5.734e+04   5.32e+04      1.078      0.281   -4.69e+04    1.62e+05
water_temp_2 water_temp_8 -3521.3203   1499.082     -2.349      0.019   -6459.497    -583.143
water_temp_2 salinity_8    5863.2156   1.25e+04      0.469      0.639   -1.87e+04    3.04e+04
salinity_2 water_temp_4   -2.978e+05   1.25e+05     -2.381      0.017   -5.43e+05   -5.27e+04
salinity_2 salinity_4     -3.135e+05   2.44e+05     -1.282      0.200   -7.93e+05    1.66e+05
salinity_2 water_temp_6     4.24e+05   1.36e+05      3.122      0.002    1.58e+05     6.9e+05
salinity_2 salinity_6      4.604e+05    3.7e+05      1.244      0.214   -2.65e+05    1.19e+06
salinity_2 water_temp_8   -1.593e+05   5.04e+04     -3.163      0.002   -2.58e+05   -6.06e+04
salinity_2 salinity_8     -1.314e+05   1.47e+05     -0.892      0.372    -4.2e+05    1.57e+05
water_temp_4 salinity_4     3.94e+05   1.62e+05      2.435      0.015    7.69e+04    7.11e+05
water_temp_4 water_temp_6 -2336.5834   1077.528     -2.168      0.030   -4448.522    -224.645
water_temp_4 salinity_6   -2.735e+05   1.23e+05     -2.215      0.027   -5.15e+05   -3.15e+04
water_temp_4 water_temp_8  4886.1956   1706.400      2.863      0.004    1541.677    8230.714
water_temp_4 salinity_8    3.531e+04    2.9e+04      1.216      0.224   -2.16e+04    9.22e+04
salinity_4 water_temp_6   -4.262e+05   1.69e+05     -2.522      0.012   -7.57e+05    -9.5e+04
salinity_4 salinity_6      -1.17e+05   8.84e+04     -1.324      0.186    -2.9e+05    5.62e+04
salinity_4 water_temp_8    1.216e+05   6.33e+04      1.920      0.055   -2506.271    2.46e+05
salinity_4 salinity_8      1.384e+05   1.02e+05      1.363      0.173   -6.06e+04    3.37e+05
water_temp_6 salinity_6     2.52e+05   1.17e+05      2.155      0.031    2.28e+04    4.81e+05
water_temp_6 water_temp_8 -2008.3934    640.127     -3.137      0.002   -3263.033    -753.754
water_temp_6 salinity_8   -4.712e+04   2.42e+04     -1.948      0.051   -9.45e+04     279.613
salinity_6 water_temp_8   -4.939e+04   4.21e+04     -1.174      0.240   -1.32e+05    3.31e+04
salinity_6 salinity_8      -3.78e+04   3.87e+04     -0.976      0.329   -1.14e+05    3.81e+04
water_temp_8 salinity_8    1.248e+04   7149.376      1.746      0.081   -1530.566    2.65e+04
==============================================================================
Omnibus:                    93894.503   Durbin-Watson:                   2.000
Prob(Omnibus):                  0.000   Jarque-Bera (JB):          1482125.420
Skew:                          -4.188   Prob(JB):                         0.00
Kurtosis:                      18.567   Cond. No.                     6.36e+09
==============================================================================

Notes:
[1] R² is computed without centering (uncentered) since the model does not contain a constant.
[2] Standard Errors assume that the covariance matrix of the errors is correctly specified.
[3] The condition number is large, 6.36e+09. This might indicate that there are
strong multicollinearity or other numerical problems.
In [64]:
fit_interaction_model(df, 'SST_C')

                                 OLS Regression Results                                
=======================================================================================
Dep. Variable:                      y   R-squared (uncentered):                   0.011
Model:                            OLS   Adj. R-squared (uncentered):              0.011
Method:                 Least Squares   F-statistic:                              23.55
Date:                Tue, 15 Jun 2021   Prob (F-statistic):                   2.84e-233
Time:                        19:58:29   Log-Likelihood:                     -7.7592e+05
No. Observations:              113837   AIC:                                  1.552e+06
Df Residuals:                  113782   BIC:                                  1.552e+06
Df Model:                          55                                                  
Covariance Type:            nonrobust                                                  
=============================================================================================
                                coef    std err          t      P>|t|      [0.025      0.975]
---------------------------------------------------------------------------------------------
water_temp_0               1397.1124   1804.293      0.774      0.439   -2139.274    4933.499
salinity_0                 -4.48e+04   4.89e+04     -0.916      0.360   -1.41e+05    5.11e+04
water_temp_2              -5291.8586   7468.038     -0.709      0.479   -1.99e+04    9345.383
salinity_2                 8.487e+04   1.13e+05      0.749      0.454   -1.37e+05    3.07e+05
water_temp_4              -6951.1520   1.89e+04     -0.368      0.713    -4.4e+04    3.01e+04
salinity_4                -3.082e+04   1.88e+05     -0.164      0.870      -4e+05    3.38e+05
water_temp_6               1.869e+04   1.94e+04      0.965      0.334   -1.93e+04    5.66e+04
salinity_6                -2.931e+04    1.6e+05     -0.183      0.855   -3.43e+05    2.84e+05
water_temp_8              -7828.4910   7273.288     -1.076      0.282   -2.21e+04    6427.043
salinity_8                 2.005e+04   4.38e+04      0.458      0.647   -6.58e+04    1.06e+05
water_temp_0 salinity_0    1554.6673   4235.273      0.367      0.714   -6746.403    9855.738
water_temp_0 water_temp_2   401.2542    268.273      1.496      0.135    -124.557     927.066
water_temp_0 salinity_2   -1.191e+04   8537.874     -1.395      0.163   -2.86e+04    4825.382
water_temp_0 water_temp_4  -649.6158   1189.611     -0.546      0.585   -2981.235    1682.004
water_temp_0 salinity_4    2922.8431   1.97e+04      0.148      0.882   -3.57e+04    4.15e+04
water_temp_0 water_temp_6  -414.9752   1580.758     -0.263      0.793   -3513.238    2683.287
water_temp_0 salinity_6    1.451e+04   1.77e+04      0.822      0.411   -2.01e+04    4.91e+04
water_temp_0 water_temp_8   711.7556    638.555      1.115      0.265    -539.802    1963.313
water_temp_0 salinity_8   -7158.8773   4214.899     -1.698      0.089   -1.54e+04    1102.261
salinity_0 water_temp_2    -1.48e+04   2.19e+04     -0.677      0.499   -5.77e+04    2.81e+04
salinity_0 salinity_2     -1.704e+04   2.49e+04     -0.685      0.493   -6.58e+04    3.17e+04
salinity_0 water_temp_4    1.419e+05    6.8e+04      2.087      0.037    8663.150    2.75e+05
salinity_0 salinity_4      2.934e+05   2.48e+05      1.182      0.237   -1.93e+05     7.8e+05
salinity_0 water_temp_6    -2.03e+05   7.11e+04     -2.854      0.004   -3.42e+05   -6.36e+04
salinity_0 salinity_6     -3.064e+05   2.98e+05     -1.029      0.304    -8.9e+05    2.77e+05
salinity_0 water_temp_8    7.476e+04    2.5e+04      2.988      0.003    2.57e+04    1.24e+05
salinity_0 salinity_8      3.097e+04   9.36e+04      0.331      0.741   -1.52e+05    2.14e+05
water_temp_2 salinity_2    4.416e+04   3.95e+04      1.117      0.264   -3.33e+04    1.22e+05
water_temp_2 water_temp_4 -1482.2232   1191.850     -1.244      0.214   -3818.231     853.784
water_temp_2 salinity_4    -9.23e+04   6.15e+04     -1.500      0.134   -2.13e+05    2.83e+04
water_temp_2 water_temp_6  4416.9555   2539.029      1.740      0.082    -559.502    9393.413
water_temp_2 salinity_6    5.737e+04   5.32e+04      1.079      0.281   -4.69e+04    1.62e+05
water_temp_2 water_temp_8 -3524.3918   1499.116     -2.351      0.019   -6462.637    -586.146
water_temp_2 salinity_8    5862.1804   1.25e+04      0.469      0.639   -1.87e+04    3.04e+04
salinity_2 water_temp_4    -2.98e+05   1.25e+05     -2.383      0.017   -5.43e+05   -5.29e+04
salinity_2 salinity_4     -3.142e+05   2.44e+05     -1.285      0.199   -7.93e+05    1.65e+05
salinity_2 water_temp_6    4.242e+05   1.36e+05      3.123      0.002    1.58e+05     6.9e+05
salinity_2 salinity_6      4.612e+05    3.7e+05      1.246      0.213   -2.64e+05    1.19e+06
salinity_2 water_temp_8   -1.593e+05   5.04e+04     -3.164      0.002   -2.58e+05   -6.06e+04
salinity_2 salinity_8     -1.315e+05   1.47e+05     -0.893      0.372    -4.2e+05    1.57e+05
water_temp_4 salinity_4    3.942e+05   1.62e+05      2.436      0.015    7.71e+04    7.11e+05
water_temp_4 water_temp_6 -2340.9298   1077.553     -2.172      0.030   -4452.917    -228.942
water_temp_4 salinity_6   -2.735e+05   1.23e+05     -2.215      0.027   -5.16e+05   -3.15e+04
water_temp_4 water_temp_8  4891.4076   1706.440      2.866      0.004    1546.811    8236.004
water_temp_4 salinity_8     3.53e+04    2.9e+04      1.216      0.224   -2.16e+04    9.22e+04
salinity_4 water_temp_6   -4.263e+05   1.69e+05     -2.523      0.012   -7.58e+05   -9.51e+04
salinity_4 salinity_6      -1.17e+05   8.84e+04     -1.323      0.186    -2.9e+05    5.63e+04
salinity_4 water_temp_8    1.216e+05   6.33e+04      1.920      0.055   -2507.794    2.46e+05
salinity_4 salinity_8      1.384e+05   1.02e+05      1.363      0.173   -6.06e+04    3.37e+05
water_temp_6 salinity_6    2.521e+05   1.17e+05      2.155      0.031    2.28e+04    4.81e+05
water_temp_6 water_temp_8 -2009.1971    640.142     -3.139      0.002   -3263.866    -754.529
water_temp_6 salinity_8   -4.711e+04   2.42e+04     -1.948      0.051   -9.45e+04     285.210
salinity_6 water_temp_8   -4.939e+04   4.21e+04     -1.174      0.240   -1.32e+05    3.31e+04
salinity_6 salinity_8     -3.789e+04   3.87e+04     -0.978      0.328   -1.14e+05    3.81e+04
water_temp_8 salinity_8    1.249e+04   7149.542      1.747      0.081   -1523.475    2.65e+04
==============================================================================
Omnibus:                    93894.534   Durbin-Watson:                   2.000
Prob(Omnibus):                  0.000   Jarque-Bera (JB):          1482127.690
Skew:                          -4.188   Prob(JB):                         0.00
Kurtosis:                      18.567   Cond. No.                     6.36e+09
==============================================================================

Notes:
[1] R² is computed without centering (uncentered) since the model does not contain a constant.
[2] Standard Errors assume that the covariance matrix of the errors is correctly specified.
[3] The condition number is large, 6.36e+09. This might indicate that there are
strong multicollinearity or other numerical problems.
In [65]:
fit_interaction_model(df, 'SAL_permil')

                                 OLS Regression Results                                
=======================================================================================
Dep. Variable:                      y   R-squared (uncentered):                   0.005
Model:                            OLS   Adj. R-squared (uncentered):              0.005
Method:                 Least Squares   F-statistic:                              11.08
Date:                Tue, 15 Jun 2021   Prob (F-statistic):                    3.10e-94
Time:                        19:58:31   Log-Likelihood:                     -7.7684e+05
No. Observations:              113837   AIC:                                  1.554e+06
Df Residuals:                  113782   BIC:                                  1.554e+06
Df Model:                          55                                                  
Covariance Type:            nonrobust                                                  
=============================================================================================
                                coef    std err          t      P>|t|      [0.025      0.975]
---------------------------------------------------------------------------------------------
water_temp_0               1367.5742   1818.942      0.752      0.452   -2197.524    4932.673
salinity_0                -4.587e+04   4.93e+04     -0.930      0.352   -1.43e+05    5.08e+04
water_temp_2              -5105.8680   7528.672     -0.678      0.498   -1.99e+04    9650.216
salinity_2                  8.92e+04   1.14e+05      0.781      0.435   -1.35e+05    3.13e+05
water_temp_4              -6757.1157   1.91e+04     -0.355      0.723   -4.41e+04    3.06e+04
salinity_4                -3.557e+04    1.9e+05     -0.187      0.851   -4.08e+05    3.36e+05
water_temp_6               1.796e+04   1.95e+04      0.920      0.357   -2.03e+04    5.62e+04
salinity_6                -2.834e+04   1.61e+05     -0.176      0.860   -3.44e+05    2.88e+05
water_temp_8              -7458.0006   7332.341     -1.017      0.309   -2.18e+04    6913.276
salinity_8                 2.057e+04   4.42e+04      0.466      0.641    -6.6e+04    1.07e+05
water_temp_0 salinity_0    1617.6373   4269.660      0.379      0.705   -6750.831    9986.105
water_temp_0 water_temp_2   401.2704    270.451      1.484      0.138    -128.810     931.351
water_temp_0 salinity_2   -1.202e+04   8607.195     -1.396      0.163   -2.89e+04    4852.843
water_temp_0 water_temp_4  -677.5743   1199.270     -0.565      0.572   -3028.125    1672.976
water_temp_0 salinity_4    2810.7528   1.99e+04      0.142      0.887   -3.61e+04    4.17e+04
water_temp_0 water_temp_6  -376.6868   1593.593     -0.236      0.813   -3500.105    2746.731
water_temp_0 salinity_6    1.461e+04   1.78e+04      0.820      0.412   -2.03e+04    4.95e+04
water_temp_0 water_temp_8   702.0970    643.739      1.091      0.275    -559.622    1963.816
water_temp_0 salinity_8   -7094.4059   4249.121     -1.670      0.095   -1.54e+04    1233.806
salinity_0 water_temp_2   -1.531e+04   2.21e+04     -0.694      0.488   -5.85e+04    2.79e+04
salinity_0 salinity_2     -1.787e+04   2.51e+04     -0.713      0.476    -6.7e+04    3.13e+04
salinity_0 water_temp_4    1.427e+05   6.85e+04      2.082      0.037    8364.997    2.77e+05
salinity_0 salinity_4      2.981e+05    2.5e+05      1.192      0.233   -1.92e+05    7.88e+05
salinity_0 water_temp_6   -2.034e+05   7.17e+04     -2.836      0.005   -3.44e+05   -6.28e+04
salinity_0 salinity_6     -3.108e+05      3e+05     -1.035      0.301   -8.99e+05    2.78e+05
salinity_0 water_temp_8    7.478e+04   2.52e+04      2.965      0.003    2.53e+04    1.24e+05
salinity_0 salinity_8      3.147e+04   9.43e+04      0.334      0.739   -1.53e+05    2.16e+05
water_temp_2 salinity_2    4.472e+04   3.98e+04      1.122      0.262   -3.34e+04    1.23e+05
water_temp_2 water_temp_4 -1451.4300   1201.527     -1.208      0.227   -3806.404     903.544
water_temp_2 salinity_4   -9.289e+04    6.2e+04     -1.497      0.134   -2.15e+05    2.87e+04
water_temp_2 water_temp_6  4369.6759   2559.643      1.707      0.088    -647.186    9386.538
water_temp_2 salinity_6    5.811e+04   5.36e+04      1.084      0.278    -4.7e+04    1.63e+05
water_temp_2 water_temp_8 -3509.7135   1511.288     -2.322      0.020   -6471.815    -547.612
water_temp_2 salinity_8    5651.7455   1.26e+04      0.448      0.654   -1.91e+04    3.04e+04
salinity_2 water_temp_4   -2.995e+05   1.26e+05     -2.375      0.018   -5.47e+05   -5.24e+04
salinity_2 salinity_4     -3.173e+05   2.46e+05     -1.287      0.198      -8e+05    1.66e+05
salinity_2 water_temp_6    4.261e+05   1.37e+05      3.112      0.002    1.58e+05    6.94e+05
salinity_2 salinity_6      4.665e+05   3.73e+05      1.250      0.211   -2.65e+05     1.2e+06
salinity_2 water_temp_8   -1.602e+05   5.08e+04     -3.156      0.002    -2.6e+05   -6.07e+04
salinity_2 salinity_8      -1.33e+05   1.48e+05     -0.896      0.370   -4.24e+05    1.58e+05
water_temp_4 salinity_4    3.971e+05   1.63e+05      2.435      0.015    7.74e+04    7.17e+05
water_temp_4 water_temp_6 -2334.6607   1086.302     -2.149      0.032   -4463.796    -205.526
water_temp_4 salinity_6   -2.762e+05   1.24e+05     -2.219      0.027    -5.2e+05   -3.22e+04
water_temp_4 water_temp_8  4883.5615   1720.295      2.839      0.005    1511.810    8255.313
water_temp_4 salinity_8    3.574e+04   2.93e+04      1.221      0.222   -2.16e+04    9.31e+04
salinity_4 water_temp_6   -4.301e+05    1.7e+05     -2.524      0.012   -7.64e+05   -9.61e+04
salinity_4 salinity_6     -1.186e+05   8.91e+04     -1.332      0.183   -2.93e+05     5.6e+04
salinity_4 water_temp_8    1.232e+05   6.39e+04      1.929      0.054   -1969.706    2.48e+05
salinity_4 salinity_8      1.386e+05   1.02e+05      1.354      0.176    -6.2e+04    3.39e+05
water_temp_6 salinity_6    2.547e+05   1.18e+05      2.161      0.031    2.37e+04    4.86e+05
water_temp_6 water_temp_8 -2006.5061    645.339     -3.109      0.002   -3271.361    -741.651
water_temp_6 salinity_8   -4.754e+04   2.44e+04     -1.950      0.051   -9.53e+04     243.333
salinity_6 water_temp_8   -5.023e+04   4.24e+04     -1.184      0.236   -1.33e+05    3.29e+04
salinity_6 salinity_8     -3.715e+04   3.91e+04     -0.951      0.342   -1.14e+05    3.94e+04
water_temp_8 salinity_8    1.262e+04   7207.590      1.750      0.080   -1509.937    2.67e+04
==============================================================================
Omnibus:                    93894.905   Durbin-Watson:                   2.000
Prob(Omnibus):                  0.000   Jarque-Bera (JB):          1482147.211
Skew:                          -4.188   Prob(JB):                         0.00
Kurtosis:                      18.567   Cond. No.                     6.36e+09
==============================================================================

Notes:
[1] R² is computed without centering (uncentered) since the model does not contain a constant.
[2] Standard Errors assume that the covariance matrix of the errors is correctly specified.
[3] The condition number is large, 6.36e+09. This might indicate that there are
strong multicollinearity or other numerical problems.
In [66]:
fit_interaction_model(df, 'fCO2_SW@SST_uatm')

                                 OLS Regression Results                                
=======================================================================================
Dep. Variable:                      y   R-squared (uncentered):                   0.551
Model:                            OLS   Adj. R-squared (uncentered):              0.550
Method:                 Least Squares   F-statistic:                              2536.
Date:                Tue, 15 Jun 2021   Prob (F-statistic):                        0.00
Time:                        19:58:32   Log-Likelihood:                     -8.1121e+05
No. Observations:              113837   AIC:                                  1.623e+06
Df Residuals:                  113782   BIC:                                  1.623e+06
Df Model:                          55                                                  
Covariance Type:            nonrobust                                                  
=============================================================================================
                                coef    std err          t      P>|t|      [0.025      0.975]
---------------------------------------------------------------------------------------------
water_temp_0               2212.4589   2460.113      0.899      0.368   -2609.326    7034.244
salinity_0                -6.252e+04   6.67e+04     -0.938      0.348   -1.93e+05    6.82e+04
water_temp_2              -5815.2583   1.02e+04     -0.571      0.568   -2.58e+04    1.41e+04
salinity_2                 9.144e+04   1.54e+05      0.592      0.554   -2.11e+05    3.94e+05
water_temp_4              -1.784e+04   2.58e+04     -0.692      0.489   -6.83e+04    3.27e+04
salinity_4                -2.075e+04   2.57e+05     -0.081      0.936   -5.24e+05    4.82e+05
water_temp_6               3.435e+04   2.64e+04      1.301      0.193   -1.74e+04    8.61e+04
salinity_6                -3.303e+04   2.18e+05     -0.151      0.880   -4.61e+05    3.94e+05
water_temp_8              -1.297e+04   9916.968     -1.308      0.191   -3.24e+04    6470.313
salinity_8                 2.489e+04   5.97e+04      0.417      0.677   -9.22e+04    1.42e+05
water_temp_0 salinity_0    1165.8460   5774.701      0.202      0.840   -1.02e+04    1.25e+04
water_temp_0 water_temp_2   654.7521    365.785      1.790      0.073     -62.180    1371.685
water_temp_0 salinity_2   -1.595e+04   1.16e+04     -1.370      0.171   -3.88e+04    6863.885
water_temp_0 water_temp_4 -1571.2084   1622.008     -0.969      0.333   -4750.320    1607.904
water_temp_0 salinity_4    3062.3239   2.68e+04      0.114      0.909   -4.96e+04    5.57e+04
water_temp_0 water_temp_6   318.6669   2155.329      0.148      0.882   -3905.746    4543.080
water_temp_0 salinity_6    2.142e+04   2.41e+04      0.889      0.374   -2.58e+04    6.86e+04
water_temp_0 water_temp_8   662.5184    870.655      0.761      0.447   -1043.952    2368.989
water_temp_0 salinity_8   -9804.9629   5746.922     -1.706      0.088   -2.11e+04    1458.918
salinity_0 water_temp_2   -1.795e+04   2.98e+04     -0.602      0.547   -7.64e+04    4.05e+04
salinity_0 salinity_2     -2.877e+04   3.39e+04     -0.848      0.396   -9.52e+04    3.77e+04
salinity_0 water_temp_4    1.895e+05   9.27e+04      2.044      0.041    7760.694    3.71e+05
salinity_0 salinity_4      4.353e+05   3.38e+05      1.286      0.198   -2.28e+05     1.1e+06
salinity_0 water_temp_6   -2.662e+05    9.7e+04     -2.745      0.006   -4.56e+05   -7.61e+04
salinity_0 salinity_6      -4.36e+05   4.06e+05     -1.074      0.283   -1.23e+06     3.6e+05
salinity_0 water_temp_8    9.415e+04   3.41e+04      2.760      0.006    2.73e+04    1.61e+05
salinity_0 salinity_8      3.081e+04   1.28e+05      0.241      0.809   -2.19e+05    2.81e+05
water_temp_2 salinity_2     5.71e+04   5.39e+04      1.059      0.289   -4.85e+04    1.63e+05
water_temp_2 water_temp_4 -1725.3101   1625.061     -1.062      0.288   -4910.405    1459.785
water_temp_2 salinity_4   -1.226e+05   8.39e+04     -1.461      0.144   -2.87e+05    4.19e+04
water_temp_2 water_temp_6  5292.1131   3461.909      1.529      0.126   -1493.177    1.21e+04
water_temp_2 salinity_6    7.466e+04   7.25e+04      1.029      0.303   -6.75e+04    2.17e+05
water_temp_2 water_temp_8 -4479.1201   2044.012     -2.191      0.028   -8485.353    -472.887
water_temp_2 salinity_8    9174.7654   1.71e+04      0.538      0.591   -2.43e+04    4.26e+04
salinity_2 water_temp_4   -3.986e+05   1.71e+05     -2.337      0.019   -7.33e+05   -6.44e+04
salinity_2 salinity_4     -4.643e+05   3.33e+05     -1.393      0.164   -1.12e+06    1.89e+05
salinity_2 water_temp_6    5.613e+05   1.85e+05      3.031      0.002    1.98e+05    9.24e+05
salinity_2 salinity_6      6.602e+05   5.05e+05      1.308      0.191   -3.29e+05    1.65e+06
salinity_2 water_temp_8    -2.05e+05   6.87e+04     -2.986      0.003    -3.4e+05   -7.04e+04
salinity_2 salinity_8     -1.687e+05   2.01e+05     -0.840      0.401   -5.62e+05    2.25e+05
water_temp_4 salinity_4    5.363e+05   2.21e+05      2.431      0.015    1.04e+05    9.69e+05
water_temp_4 water_temp_6 -3086.4830   1469.220     -2.101      0.036   -5966.132    -206.835
water_temp_4 salinity_6   -3.729e+05   1.68e+05     -2.215      0.027   -7.03e+05   -4.29e+04
water_temp_4 water_temp_8  7014.3330   2326.693      3.015      0.003    2454.050    1.16e+04
water_temp_4 salinity_8    4.576e+04   3.96e+04      1.156      0.248   -3.18e+04    1.23e+05
salinity_4 water_temp_6   -5.841e+05    2.3e+05     -2.535      0.011   -1.04e+06   -1.32e+05
salinity_4 salinity_6     -1.664e+05   1.21e+05     -1.380      0.167   -4.03e+05    6.98e+04
salinity_4 water_temp_8    1.678e+05   8.64e+04      1.943      0.052   -1505.552    3.37e+05
salinity_4 salinity_8      1.955e+05   1.38e+05      1.412      0.158   -7.58e+04    4.67e+05
water_temp_6 salinity_6    3.524e+05   1.59e+05      2.210      0.027    3.99e+04    6.65e+05
water_temp_6 water_temp_8 -3079.5403    872.820     -3.528      0.000   -4790.253   -1368.827
water_temp_6 salinity_8   -6.394e+04    3.3e+04     -1.939      0.052   -1.29e+05     687.747
salinity_6 water_temp_8   -7.472e+04   5.74e+04     -1.302      0.193   -1.87e+05    3.77e+04
salinity_6 salinity_8     -5.775e+04   5.28e+04     -1.093      0.274   -1.61e+05    4.58e+04
water_temp_8 salinity_8    1.808e+04   9748.243      1.855      0.064   -1028.087    3.72e+04
==============================================================================
Omnibus:                    93825.981   Durbin-Watson:                   1.999
Prob(Omnibus):                  0.000   Jarque-Bera (JB):          1479200.544
Skew:                          -4.184   Prob(JB):                         0.00
Kurtosis:                      18.551   Cond. No.                     6.36e+09
==============================================================================

Notes:
[1] R² is computed without centering (uncentered) since the model does not contain a constant.
[2] Standard Errors assume that the covariance matrix of the errors is correctly specified.
[3] The condition number is large, 6.36e+09. This might indicate that there are
strong multicollinearity or other numerical problems.
In [67]:
fit_interaction_model(df, 'fCO2_ATM_interpolated_uatm')

                                 OLS Regression Results                                
=======================================================================================
Dep. Variable:                      y   R-squared (uncentered):                   0.550
Model:                            OLS   Adj. R-squared (uncentered):              0.550
Method:                 Least Squares   F-statistic:                              2529.
Date:                Tue, 15 Jun 2021   Prob (F-statistic):                        0.00
Time:                        19:58:34   Log-Likelihood:                     -8.1119e+05
No. Observations:              113837   AIC:                                  1.622e+06
Df Residuals:                  113782   BIC:                                  1.623e+06
Df Model:                          55                                                  
Covariance Type:            nonrobust                                                  
=============================================================================================
                                coef    std err          t      P>|t|      [0.025      0.975]
---------------------------------------------------------------------------------------------
water_temp_0               2112.8658   2459.590      0.859      0.390   -2707.892    6933.624
salinity_0                -5.038e+04   6.67e+04     -0.756      0.450   -1.81e+05    8.03e+04
water_temp_2              -8036.4936   1.02e+04     -0.789      0.430    -2.8e+04    1.19e+04
salinity_2                 1.115e+05   1.54e+05      0.722      0.471   -1.91e+05    4.14e+05
water_temp_4              -1.029e+04   2.58e+04     -0.399      0.690   -6.08e+04    4.02e+04
salinity_4                -5.187e+04   2.57e+05     -0.202      0.840   -5.55e+05    4.51e+05
water_temp_6               2.636e+04   2.64e+04      0.999      0.318   -2.54e+04    7.81e+04
salinity_6                  -4.5e+04   2.18e+05     -0.206      0.837   -4.72e+05    3.82e+05
water_temp_8              -1.016e+04   9914.856     -1.025      0.306   -2.96e+04    9274.128
salinity_8                 3.581e+04   5.97e+04      0.600      0.549   -8.12e+04    1.53e+05
water_temp_0 salinity_0    1642.6484   5773.472      0.285      0.776   -9673.269     1.3e+04
water_temp_0 water_temp_2   576.2747    365.707      1.576      0.115    -140.505    1293.055
water_temp_0 salinity_2   -1.547e+04   1.16e+04     -1.329      0.184   -3.83e+04    7342.816
water_temp_0 water_temp_4  -634.2707   1621.663     -0.391      0.696   -3812.706    2544.164
water_temp_0 salinity_4    3850.4720   2.68e+04      0.143      0.886   -4.88e+04    5.65e+04
water_temp_0 water_temp_6 -1002.1520   2154.870     -0.465      0.642   -5225.665    3221.361
water_temp_0 salinity_6    1.957e+04   2.41e+04      0.813      0.416   -2.76e+04    6.68e+04
water_temp_0 water_temp_8  1126.2526    870.470      1.294      0.196    -579.855    2832.360
water_temp_0 salinity_8   -9710.1713   5745.699     -1.690      0.091    -2.1e+04    1551.311
salinity_0 water_temp_2   -1.972e+04   2.98e+04     -0.661      0.508   -7.82e+04    3.87e+04
salinity_0 salinity_2     -2.409e+04   3.39e+04     -0.710      0.477   -9.05e+04    4.24e+04
salinity_0 water_temp_4    1.944e+05   9.27e+04      2.097      0.036    1.27e+04    3.76e+05
salinity_0 salinity_4      4.017e+05   3.38e+05      1.188      0.235   -2.61e+05    1.06e+06
salinity_0 water_temp_6   -2.795e+05    9.7e+04     -2.883      0.004    -4.7e+05   -8.95e+04
salinity_0 salinity_6     -4.147e+05   4.06e+05     -1.021      0.307   -1.21e+06    3.81e+05
salinity_0 water_temp_8    1.037e+05   3.41e+04      3.040      0.002    3.69e+04    1.71e+05
salinity_0 salinity_8      3.805e+04   1.28e+05      0.298      0.766   -2.12e+05    2.88e+05
water_temp_2 salinity_2    5.696e+04   5.39e+04      1.057      0.290   -4.87e+04    1.63e+05
water_temp_2 water_temp_4 -2323.8473   1624.715     -1.430      0.153   -5508.264     860.569
water_temp_2 salinity_4   -1.199e+05   8.39e+04     -1.429      0.153   -2.84e+05    4.45e+04
water_temp_2 water_temp_6  6358.1298   3461.172      1.837      0.066    -425.716    1.31e+04
water_temp_2 salinity_6    7.407e+04   7.25e+04      1.022      0.307    -6.8e+04    2.16e+05
water_temp_2 water_temp_8 -4858.7974   2043.577     -2.378      0.017   -8864.178    -853.417
water_temp_2 salinity_8    8993.9181   1.71e+04      0.527      0.598   -2.44e+04    4.24e+04
salinity_2 water_temp_4   -3.993e+05   1.71e+05     -2.342      0.019   -7.33e+05   -6.51e+04
salinity_2 salinity_4     -4.316e+05   3.33e+05     -1.295      0.195   -1.08e+06    2.22e+05
salinity_2 water_temp_6    5.785e+05   1.85e+05      3.124      0.002    2.16e+05    9.41e+05
salinity_2 salinity_6      6.306e+05   5.05e+05      1.249      0.211   -3.59e+05    1.62e+06
salinity_2 water_temp_8   -2.221e+05   6.86e+04     -3.235      0.001   -3.57e+05   -8.75e+04
salinity_2 salinity_8     -1.769e+05   2.01e+05     -0.881      0.378    -5.7e+05    2.17e+05
water_temp_4 salinity_4    5.172e+05   2.21e+05      2.345      0.019    8.49e+04     9.5e+05
water_temp_4 water_temp_6 -3063.0230   1468.907     -2.085      0.037   -5942.058    -183.988
water_temp_4 salinity_6   -3.597e+05   1.68e+05     -2.137      0.033    -6.9e+05   -2.98e+04
water_temp_4 water_temp_8  6592.5155   2326.198      2.834      0.005    2033.203    1.12e+04
water_temp_4 salinity_8    4.717e+04   3.96e+04      1.192      0.233   -3.04e+04    1.25e+05
salinity_4 water_temp_6    -5.66e+05    2.3e+05     -2.457      0.014   -1.02e+06   -1.14e+05
salinity_4 salinity_6     -1.617e+05    1.2e+05     -1.342      0.179   -3.98e+05    7.44e+04
salinity_4 water_temp_8    1.652e+05   8.63e+04      1.914      0.056   -4000.744    3.34e+05
salinity_4 salinity_8      1.926e+05   1.38e+05      1.391      0.164   -7.87e+04    4.64e+05
water_temp_6 salinity_6    3.298e+05   1.59e+05      2.069      0.039    1.73e+04    6.42e+05
water_temp_6 water_temp_8 -2771.1658    872.634     -3.176      0.001   -4481.515   -1060.817
water_temp_6 salinity_8   -6.316e+04    3.3e+04     -1.916      0.055   -1.28e+05    1449.655
salinity_6 water_temp_8   -6.248e+04   5.74e+04     -1.089      0.276   -1.75e+05    4.99e+04
salinity_6 salinity_8     -5.406e+04   5.28e+04     -1.024      0.306   -1.58e+05    4.95e+04
water_temp_8 salinity_8    1.586e+04   9746.168      1.627      0.104   -3243.654     3.5e+04
==============================================================================
Omnibus:                    93857.225   Durbin-Watson:                   1.999
Prob(Omnibus):                  0.000   Jarque-Bera (JB):          1480208.951
Skew:                          -4.186   Prob(JB):                         0.00
Kurtosis:                      18.556   Cond. No.                     6.36e+09
==============================================================================

Notes:
[1] R² is computed without centering (uncentered) since the model does not contain a constant.
[2] Standard Errors assume that the covariance matrix of the errors is correctly specified.
[3] The condition number is large, 6.36e+09. This might indicate that there are
strong multicollinearity or other numerical problems.
In [68]:
fit_interaction_model(df, 'dfCO2_uatm')

                                 OLS Regression Results                                
=======================================================================================
Dep. Variable:                      y   R-squared (uncentered):                   0.058
Model:                            OLS   Adj. R-squared (uncentered):              0.057
Method:                 Least Squares   F-statistic:                              127.0
Date:                Tue, 15 Jun 2021   Prob (F-statistic):                        0.00
Time:                        19:58:35   Log-Likelihood:                     -7.7291e+05
No. Observations:              113837   AIC:                                  1.546e+06
Df Residuals:                  113782   BIC:                                  1.546e+06
Df Model:                          55                                                  
Covariance Type:            nonrobust                                                  
=============================================================================================
                                coef    std err          t      P>|t|      [0.025      0.975]
---------------------------------------------------------------------------------------------
water_temp_0               1450.2732   1757.189      0.825      0.409   -1993.792    4894.338
salinity_0                -5.569e+04   4.76e+04     -1.169      0.242   -1.49e+05    3.77e+04
water_temp_2              -2863.8993   7273.076     -0.394      0.694   -1.71e+04    1.14e+04
salinity_2                 6.325e+04    1.1e+05      0.573      0.566   -1.53e+05     2.8e+05
water_temp_4              -1.416e+04   1.84e+04     -0.769      0.442   -5.02e+04    2.19e+04
salinity_4                 -350.4962   1.83e+05     -0.002      0.998    -3.6e+05    3.59e+05
water_temp_6               2.586e+04   1.89e+04      1.371      0.170   -1.11e+04    6.28e+04
salinity_6                -1.581e+04   1.56e+05     -0.102      0.919   -3.21e+05     2.9e+05
water_temp_8              -1.032e+04   7083.410     -1.457      0.145   -2.42e+04    3559.641
salinity_8                 8604.7319   4.27e+04      0.202      0.840    -7.5e+04    9.22e+04
water_temp_0 salinity_0    1078.0125   4124.706      0.261      0.794   -7006.349    9162.374
water_temp_0 water_temp_2   468.8477    261.270      1.794      0.073     -43.237     980.932
water_temp_0 salinity_2    -1.21e+04   8314.983     -1.456      0.145   -2.84e+04    4193.362
water_temp_0 water_temp_4 -1577.1470   1158.555     -1.361      0.173   -3847.897     693.603
water_temp_0 salinity_4    1977.1643   1.92e+04      0.103      0.918   -3.56e+04    3.96e+04
water_temp_0 water_temp_6   927.4705   1539.491      0.602      0.547   -2089.908    3944.849
water_temp_0 salinity_6    1.599e+04   1.72e+04      0.929      0.353   -1.77e+04    4.97e+04
water_temp_0 water_temp_8   226.7103    621.884      0.365      0.715    -992.173    1445.594
water_temp_0 salinity_8   -7014.7573   4104.864     -1.709      0.087   -1.51e+04    1030.714
salinity_0 water_temp_2   -1.294e+04   2.13e+04     -0.607      0.544   -5.47e+04    2.88e+04
salinity_0 salinity_2     -2.149e+04   2.42e+04     -0.887      0.375    -6.9e+04     2.6e+04
salinity_0 water_temp_4    1.335e+05   6.62e+04      2.015      0.044    3662.969    2.63e+05
salinity_0 salinity_4      3.186e+05   2.42e+05      1.318      0.187   -1.55e+05    7.92e+05
salinity_0 water_temp_6   -1.843e+05   6.93e+04     -2.660      0.008    -3.2e+05   -4.85e+04
salinity_0 salinity_6      -3.19e+05    2.9e+05     -1.100      0.272   -8.88e+05     2.5e+05
salinity_0 water_temp_8    6.316e+04   2.44e+04      2.592      0.010    1.54e+04    1.11e+05
salinity_0 salinity_8      2.301e+04   9.11e+04      0.253      0.801   -1.56e+05    2.02e+05
water_temp_2 salinity_2    4.339e+04   3.85e+04      1.127      0.260   -3.21e+04    1.19e+05
water_temp_2 water_temp_4  -827.9033   1160.735     -0.713      0.476   -3102.926    1447.120
water_temp_2 salinity_4   -9.226e+04   5.99e+04     -1.539      0.124    -2.1e+05    2.52e+04
water_temp_2 water_temp_6  3203.3217   2472.744      1.295      0.195   -1643.219    8049.863
water_temp_2 salinity_6    5.623e+04   5.18e+04      1.085      0.278   -4.53e+04    1.58e+05
water_temp_2 water_temp_8 -3036.7200   1459.980     -2.080      0.038   -5898.259    -175.181
water_temp_2 salinity_8    5810.8084   1.22e+04      0.477      0.633   -1.81e+04    2.97e+04
salinity_2 water_temp_4   -2.896e+05   1.22e+05     -2.378      0.017   -5.28e+05   -5.09e+04
salinity_2 salinity_4     -3.372e+05   2.38e+05     -1.416      0.157   -8.04e+05     1.3e+05
salinity_2 water_temp_6    3.958e+05   1.32e+05      2.992      0.003    1.37e+05    6.55e+05
salinity_2 salinity_6      4.776e+05   3.61e+05      1.325      0.185   -2.29e+05    1.18e+06
salinity_2 water_temp_8   -1.382e+05    4.9e+04     -2.817      0.005   -2.34e+05    -4.2e+04
salinity_2 salinity_8     -1.201e+05   1.43e+05     -0.837      0.403   -4.01e+05    1.61e+05
water_temp_4 salinity_4    4.021e+05   1.58e+05      2.552      0.011    9.32e+04    7.11e+05
water_temp_4 water_temp_6 -2290.3829   1049.422     -2.183      0.029   -4347.234    -233.531
water_temp_4 salinity_6   -2.787e+05    1.2e+05     -2.318      0.020   -5.14e+05    -4.3e+04
water_temp_4 water_temp_8  5160.1883   1661.891      3.105      0.002    1902.907    8417.470
water_temp_4 salinity_8    3.288e+04   2.83e+04      1.163      0.245   -2.25e+04    8.83e+04
salinity_4 water_temp_6   -4.328e+05   1.65e+05     -2.630      0.009   -7.55e+05    -1.1e+05
salinity_4 salinity_6     -1.188e+05   8.61e+04     -1.380      0.168   -2.87e+05    4.99e+04
salinity_4 water_temp_8    1.211e+05   6.17e+04      1.963      0.050     214.063    2.42e+05
salinity_4 salinity_8      1.372e+05   9.89e+04      1.387      0.165   -5.66e+04    3.31e+05
water_temp_6 salinity_6    2.674e+05   1.14e+05      2.348      0.019    4.41e+04    4.91e+05
water_temp_6 water_temp_8 -2253.5502    623.430     -3.615      0.000   -3475.464   -1031.636
water_temp_6 salinity_8   -4.649e+04   2.36e+04     -1.974      0.048   -9.26e+04    -329.887
salinity_6 water_temp_8   -6.024e+04    4.1e+04     -1.470      0.142   -1.41e+05    2.01e+04
salinity_6 salinity_8         -4e+04   3.77e+04     -1.060      0.289   -1.14e+05     3.4e+04
water_temp_8 salinity_8    1.433e+04   6962.895      2.058      0.040     679.621     2.8e+04
==============================================================================
Omnibus:                    93725.391   Durbin-Watson:                   2.000
Prob(Omnibus):                  0.000   Jarque-Bera (JB):          1475107.402
Skew:                          -4.178   Prob(JB):                         0.00
Kurtosis:                      18.530   Cond. No.                     6.36e+09
==============================================================================

Notes:
[1] R² is computed without centering (uncentered) since the model does not contain a constant.
[2] Standard Errors assume that the covariance matrix of the errors is correctly specified.
[3] The condition number is large, 6.36e+09. This might indicate that there are
strong multicollinearity or other numerical problems.
In [45]:
import xgboost as xgb
import matplotlib.pyplot as plt

params = {
    'max_depth':    4,
    'max_leaves':   2**8,
    'tree_method':  'gpu_hist',
    'objective':    'reg:squarederror',
    'grow_policy':  'lossguide',
    'eval_metric':  'logloss',
    'subsample':    '0.8'
}

def fit_interaction_model(df, pred_col, n_interaction=2):
    
    df = df.dropna()
    
    X = df[X_col_names]
    y = df[[pred_col]]
    
    poly_features = PolynomialFeatures(n_interaction, interaction_only=True, include_bias=False) 
    X_inter = poly_features.fit_transform(X.as_gpu_matrix())
    X_df = cudf.DataFrame(X_inter, columns=poly_features.get_feature_names(X.columns))
    
    dtrain = xgb.DMatrix(X_df, y)

    model = xgb.train(params, dtrain, num_boost_round=100)

    scores = dict(sorted(model.get_score(importance_type='gain').items(), key=lambda item: item[1], reverse=True))
    scores = pd.DataFrame.from_dict(scores, orient='index').reset_index()
    scores.columns = ['interaction', 'F-score']
    return scores
In [46]:
fit_interaction_model(df, 'xCO2_EQU_ppm')
Out[46]:
interaction F-score
0 salinity_4 water_temp_6 4.430559e+06
1 water_temp_4 salinity_6 3.796217e+06
2 salinity_0 water_temp_2 2.795584e+06
3 water_temp_2 salinity_8 2.777022e+06
4 salinity_0 water_temp_4 2.664439e+06
5 salinity_4 2.586490e+06
6 salinity_6 water_temp_8 2.442660e+06
7 water_temp_4 2.351526e+06
8 water_temp_4 salinity_4 2.331590e+06
9 salinity_2 2.326387e+06
10 water_temp_0 salinity_6 2.146548e+06
11 water_temp_6 salinity_6 2.128905e+06
12 water_temp_4 water_temp_8 2.027545e+06
13 water_temp_2 salinity_4 1.974119e+06
14 water_temp_0 water_temp_6 1.959638e+06
15 water_temp_0 salinity_0 1.939111e+06
16 salinity_0 salinity_8 1.904266e+06
17 water_temp_2 salinity_6 1.900974e+06
18 water_temp_2 1.889223e+06
19 salinity_4 salinity_6 1.842115e+06
20 water_temp_2 salinity_2 1.831252e+06
21 water_temp_0 water_temp_8 1.813927e+06
22 salinity_0 water_temp_8 1.809904e+06
23 water_temp_2 water_temp_8 1.804140e+06
24 water_temp_0 water_temp_4 1.791293e+06
25 water_temp_2 water_temp_6 1.768099e+06
26 salinity_0 salinity_4 1.760418e+06
27 water_temp_0 water_temp_2 1.743686e+06
28 salinity_0 salinity_6 1.733822e+06
29 salinity_0 1.721878e+06
30 salinity_2 water_temp_6 1.697035e+06
31 water_temp_4 water_temp_6 1.664098e+06
32 water_temp_0 1.654031e+06
33 salinity_2 salinity_4 1.650368e+06
34 water_temp_0 salinity_2 1.637497e+06
35 salinity_4 salinity_8 1.601531e+06
36 salinity_2 water_temp_4 1.593254e+06
37 water_temp_8 salinity_8 1.584930e+06
38 water_temp_6 water_temp_8 1.463999e+06
39 salinity_2 water_temp_8 1.455252e+06
40 salinity_6 salinity_8 1.451010e+06
41 salinity_6 1.399099e+06
42 salinity_8 1.385359e+06
43 water_temp_6 salinity_8 1.384313e+06
44 water_temp_0 salinity_8 1.363816e+06
45 water_temp_8 1.350263e+06
46 salinity_0 salinity_2 1.342739e+06
47 salinity_4 water_temp_8 1.282066e+06
48 salinity_0 water_temp_6 1.267655e+06
49 water_temp_6 1.216087e+06
50 water_temp_0 salinity_4 1.138838e+06
51 water_temp_4 salinity_8 1.137954e+06
52 salinity_2 salinity_8 1.067442e+06
53 water_temp_2 water_temp_4 9.797247e+05
54 salinity_2 salinity_6 7.626201e+05